Question: Michael is 3 times as old as Ashley. Eight years ago, Michael was 7 times as old as Ashley. How old is Michael now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Ashley. Let Michael's current age be $m$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $m = 3a$ Eight years ago, Michael was $m - 8$ years old, and Ashley was $a - 8$ years old. The information in the second sentence can be expressed in the following equation: $m - 8 = 7(a - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = m / 3$ . Substituting this into our second equation, we get: $m - 8 = 7($ $(m / 3)$ $- 8)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 8 = \dfrac{7}{3} m - 56$ Solving for $m$ , we get: $\dfrac{4}{3} m = 48$ $m = \dfrac{3}{4} \cdot 48 = 36$.